Why Corsi numbers are an unreliable base stat for rating players

Corsi fixes one major problem with on-ice plus-minus, but fails to fix the second big one…

The concept of rating hockey players through Corsi, a measure of each player’s shots-at-net plus-minus at even strength, is an excellent one in theory.

In practice, however, using the standard tools available in 2013 for Corsi analysis, employing on-ice shots-at-net numbers to rate NHL players is problematic. It often leads to unfair and inaccurate judgments. NHL general managers will find this out for themselves if they rely too much on this advanced stat metric to make personnel decisions.

Corsi does have its strength. It corrects one of the major problems of the NHL’s official plus-minus system, the lack of sample size that comes with goals plus-minus. Corsi does so by tracking not goals, but shots-at-net, a far more common event in a game than goals. This greatly increases Corsi’s sample size and its accuracy. At the same time, however, Corsi fails to fix the other other major problem with official plus-minus, the high percentage of false positive and negatives handed out in on-ice plus-minus systems.

Let’s say a player is out on the ice for 30 shots at net for in a game and 20 shots at net against. The player is a defensive defenceman and he only helped to create 5 of those shots at net, while he made mistakes that led to 15 shots at net against. His real impact on the game is -10 Corsi, but the mechanical system now being used would give him a +10 Corsi plus-minus. He got that positive mark only because he was on the ice with better players who created a positive but unearned differential for him. This same dynamic can happen game after game, month after month, giving a player an unfair and inaccurate Corsi rating over a full season.

A good player playing consistently with bad players will get hammered by Corsi, while a good player playing with great ones will get a boost.

This is a massive flaw in the way Corsi is generally used right now, but not fatal to the Corsi concept itself, which might one day be coupled with intensive video analysis to provide a superior plus-minus metric.

The Roth-Irvin system

In the late 1940s, Montreal Canadiens coach Dick Irvin Sr. and Montreal tie salesman Allan Roth developed the NHL’s first plus-minus system by giving a plus mark to every player on the ice for a goal for and a minus mark for every player on the ice for a goal against.

This system, brilliant in its day, has two problems.

First, goals are so rare that even over a full season of play, a player who is playing strong hockey might be on the ice for many more goals against than he is on for goals for. For example, he might have been out there when his team constantly hit the post, while the other team was constantly ringing in shots off the post for goals. It’s been known to happen. In fact, it’s not uncommon, and due to the scarcity of goals, if a player is out for 10 bad luck goals against, while not any good luck goals going his way, his official plus-minus can be skewed. Many good two-way hockey players have ended up with nasty negative Roth-Irvin plus-minus numbers in this manner.

The Corsi system fixes this problem by counting up an on-ice event other than the goal, but an event that is also important to winning hockey games, the shot-at-net. Of course, goals are far more important than shots-at-net to a team’s success, but shots-at-net should not be under-estimated. A team that regularly outshoots its opponents is usually a winning team. Shots-at-net mean time in the offensive end and that lead to goals.

If a player is out for many, many shots-at-net for, he’s spending a lot of time in the opposition end of the ice, which is a very good place for a player to be in a hockey game. If he’s out for a lot of shots against, he’s in his own end a lot, not such a good place to be. If his team regularly has 15 shots-at-net when he’s on the ice during a game, and gives up just 10 shots-at-net against, something is definitely going right when that player is on the ice. And because a player is out on the ice for so many more shots-at-net than goals during a full season of play, Corsi takes much of the luck out of the equation for measuring players.

That’s good. That makes Corsi useful, in theory.

However, it still has the same major problem as the Roth-Irvin system in one other regard: since every player on the ice gets a plus or a minus after each shot-at-net, Corsi awards plus marks to players even if they did nothing to help create the shot-at net, and the system assigns minus marks to players who made no mistake on the shot-at-net against. The current system assigns these unearned marks at a high rate, likely around 40 per cent of the time.

At times, Corsi plus-minus still gets it somewhat right in rating players, even as it is imprecise. It’s certainly a better way to rate players than using official plus-minus. But this kind of inaccuracy, this high rate of false positives and false negatives, can leads to wonky results — and the biggest problem with Corsi is you can never tell from just looking at an individual player’s rating if Corsi has rated him accurately or inaccurately. The numbers are silent on that, just as official plus-minus is silent on which players got lucky or unlucky.

Mark Fistric Case Study

Take the case of Oilers defenceman and currently unsigned NHL free agent Mark Fistric.

Of all the regular defenceman (more than 20 games played) in the NHL, only 33 had better Relative Corsi numbers than Fistric last season, according to Behind the Net.

In the list of Top Ten defenceman at even strength according to Relative Corsi, we also find Jake Muzzin, Marc-Andre Bergeron, Thomas Hickey, Bobby Sanguinetti, and Radko Gudas, names not generally associated with the top two-way or puck possession defencemen in the NHL. In fact, many ahead of Fistric in the rankings are marginal NHLers, just like Fistric himself.

On his own Oilers squad, Fistric had the single best Corsi of any defenceman, beating out noted skaters and puckhandlers like Justin Schultz and Jeff Petry.

If you’ve watched Fistric play — whatever his Corsi number might hint at — you’ll note that he’s not much when it comes to passing and shooting. I don’t mind his game and he certainly didn’t kill the OIlers last year. He’s a decent positional defender and a hard hitter. But his puck possession game is weak.

Don’t believe me?

Two close observers of the game who used video analysis to measure puck movement through Zone Exit and Zone Entry studies found Fistric not to be best Oilers d-man when it came to puck possession, but the worst.

The Cult’s Bruce McCurdy found that Fistric was the least likely Oilers defenceman to get the puck out of the Oilers zone under control and the least likely to get it out period. And The Cult’s Jonathan Willisfound that Fistric was the least likely Oilers defencemanto advance the puck into the opposition end under control or advance it period.

As I said, Fistric will knock you cold if you don’t keep your head up, but he’s not going to beat you with his skating and passing. How is it then that Fistric’s Corsi number — which is generally deemed to have some relationship to puck possession — is so out of whack with Fistric’s actual performance?

Let’s dig into Fistric’s Corsi number, his shots-at-net plus-minus, to see why it might be so high in comparison to other Oilers defenders and on a relative basis to other NHL defencemen.

Breaking Down Fistric’s Corsi

Fistric played 330 even strength minutes in 2013.

When he was on the ice in 5-on-5 play (which would be almost all of his even strength minutes so I’ll be basing my calculations here on that assumption), the Oilers outshot the opposition, 26.3 to 25.0 per 60 minutes of play.

It was only when Fistric was on the ice that the Oilers outshot the opposition in five-on-five play.

He was on the ice for 146 shots for and 138 against.

He was on the ice for 11 goals for and 8 goals against.

He was on the ice for 63 missed shots for and 63 missed shots against.

He was on the ice when the Oilers had 61 of their shots blocked and blocked 109 shots.

Add it all up and Fistric was on the ice for 281 shots-at-net for and 318 shots-at-net against.

Overall, for the entire year, he was -37 for shots-at-net (Corsi) plus-minus, not good, but not bad on a team that got badly outshot at even strength and better than any other fulltime Oilers d-man.

Fistric’s real contribution to shots-at-net

The key question in judging Fistric’s puck possession prowess isn’t how many shots-at-net he was simply on the ice for, it’s how many of those shots for he actually had a hand in creating and how many of the shots against he made some mistake on.

Just because a player is out on the ice it doesn’t mean he contributes to all the events that happen when he’s out there. A goal may be scored, a hit may happen, a fight may occur, a great play, a terrible play, and the player in question may well have been an innocent bystander.

No one has gone through the video and counted up how many of shots at net for and against Fistric was in any way responsible for. If they did that work, that would be a useful and valid way to rate Fistric’s puck possession skills. That would be a proper use of Corsi. But all we have now from his published Corsi data is somewhat vague circumstantial evidence.

In total, he made some pass, hit, screen or hit that helped to create 31 scoring chances for at even strength. And he made some mistake — a missed assignment, a lost battle or a turnover — that contributed to 48 scoring chances against.

When you look at scoring chances as way to measure puck possession, you find that Fistric wasn’t the best Oilers defenceman, he was actually the worst when it came to creating scoring chances, while he actually did OK when it came to preventing them.

When it came to contributing to scoring chances, Justin Schultz was at 2.4 per 15 minutes of even strength play, Nick Schultz, 2.1 per 15, Ryan Whitney and Corey Potter, 1.9 per 15, Jeff Petry, 1.8 per 15, Ladi Smid, 1.7 per 15, and Fistric, 1.4 per 15.

This lack of measurable offensive prowess lines up exactly with what Willis and McCurdy found. When it came to moving the puck, Fistric wasn’t the best Oilers d-man, he was the worst, which likely explains why the Oilers and other NHL teams have yet to offer him a contract.

When it came to making mistakes on scoring chances against, Whitney was the worst with 3.0 per 15, then Jeff Petry, 2.7 per 15, Nick Schultz, 2.5 per 15, Justin Schultz and Ladi Smid, 2.3 per 15, Fistric, 2.2 per 15 and Corey Potter, 1.8 per 15.

In the end, Fistric was on the ice for 281 shots-at-net at even strength, but he only made some contribution to an actual scoring chance on 31 of those 281 shots, and he only made a mistake on a scoring chance against on 48 of the 318 shots-at-net against he was on the ice for.

It’s a safe bet that Fistric’s ratio of shots-at-net for to shots-at-net against is close to him chipping in on 3 out of 10 shots for, while making mistakes on 5 out of 10 shots against, just as he did with scoring chances. If you watched the video, and tabulated the actual individual contributions to Corsi numbers for and against, Fistric;s plus-minus would be much more in the negative column, maybe not as bad as Ryan Whitney, but close to it. Fistric’s accurate Corsi is probably around -100, not -39.

Fistric’s Corsi stats in context with QualComp and ZS

One thing that the many Corsi advocates bring up is that you have to put a player’s shots-at-net plus-minus in context, factoring in Quality of Competition and ZoneStarts. Of course, you need to put all stats in this kind of context, including the scoring chance data I collect, or basic goal scoring data collected by the NHL. Corsi numbers aren’t special in this regard. All stats need context, but they still will only make sense if they’re not riddled with false positives and negatives to begin with.

There’s no doubt that quality of competition impacts all stats, goals, scoring chances, shots-at-net. In this regard, Fistric faced almost the same quality of competition as did Whitney, and only Corey Potter faced easier quality of competition for Oilers d-men. Petry and Smid faced the toughest quality of competition, and it certainly impacted all their stats, including their scoring chances plus-minus.

When it comes to Fistric, all kinds of other players who faced similarly weak quality of competition on the Oilers, such as Ryan Whitney, Eric Belanger, Nail Yakupov and Ryan Smyth had bad shots-at-net (Corsi) plus-minus numbers. Fistric stands out from that group. He’s the one who was able to have a strong shots-at-net plus-minus, while the others failed, and he’s the one who did it despite tough faceoff assignments.

Either we accept that Fistric is a good puck possession d-man or we accept that Corsi numbers aren’t that accurate in rating puck possession, at least the way they’re employed now, without further video analysis to pinpoint the exact contributions of players.

This same 30 per cent false positive and 50 per cent false negative ratio almost certainly applies to shots-at-net for and against, and is likely higher on shot counts, given that goals tend to come from slightly or greatly more involved sequences of play than mere shots.

But if 40 per cent of the time a player is getting a plus or minus mark he doesn’t merit, that builds in a lot of error and randomness into a system of rating a player. That is what Corsi does.

And, for that reason, Corsi is an unreliable base stat to use in rating players. It’s better than Roth-Irvin, but still has one of the same big warts.

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